If a right triangle has an angle that is 65°, what is the third angle in the triangle? (1 point)
The sum of the angles in a triangle is always 180 degrees.
Given that one angle is 65°, we can find the third angle by subtracting the sum of the other two angles from 180°.
So, the third angle in the triangle would be 180° - (90° + 65°) = 180° - 155° = 25°.
If a triangle has sides measuring 60, 75, and 45, is it a right triangle? (1 point)
• Yes, because 5,625 equals 5,625.
• Yes, because 3,600 equals 3,600.
O No, because 9,225 does not equal 2,025.
O. No, because 5,625 does not equal 3,600.
To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the sides of the triangle measure 60, 75, and 45. We need to check if 60^2 + 45^2 = 75^2.
60^2 + 45^2 = 3600 + 2025 = 5625
Since 5625 does not equal 75^2 (which is equal to 5625), the triangle is not a right triangle.
Therefore, the correct answer is:
No, because 5,625 does not equal 3,600.
If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0. (1 point)
To determine if a triangle is a right triangle, we can again use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the sides of the triangle measure 50, 40, and 32. We need to check if 32^2 + 40^2 = 50^2.
32^2 + 40^2 = 1024 + 1600 = 2624
Since 2624 does not equal 50^2 (which is equal to 2500), the triangle is not a right triangle.
Therefore, the correct answer is:
0
If a triangle has sides of length 12 and 16, how long is the hypotenuse? (1 point)
To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the sides of the triangle measure 12 and 16. We need to find the length of the hypotenuse.
The length of the hypotenuse can be found by taking the square root of the sum of the squares of the other two sides.
Hypotenuse^2 = 12^2 + 16^2
Hypotenuse^2 = 144 + 256
Hypotenuse^2 = 400
Taking the square root of both sides, we have:
Hypotenuse = √400
Simplifying, we have:
Hypotenuse = 20
Therefore, the length of the hypotenuse is 20.
If a right triangle has a leg with length 12 and the hypotenuse is 16, how long is the other leg? Round to the nearest tenth, if necessary. (1 point)
To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the leg length is given as 12 and the hypotenuse is 16. We need to find the length of the other leg.
The other leg can be found by taking the square root of the difference between the square of the hypotenuse and the square of the given leg.
Other leg^2 = hypotenuse^2 - given leg^2
Other leg^2 = 16^2 - 12^2
Other leg^2 = 256 - 144
Other leg^2 = 112
Taking the square root of both sides, we have:
Other leg = √112
Simplifying and rounding to the nearest tenth, we have:
Other leg ≈ 10.6
Therefore, the length of the other leg is approximately 10.6 units.